Problem: $ B = \left[\begin{array}{rr}4 & 1 \\ 2 & -1\end{array}\right]$ $ A = \left[\begin{array}{r}0 \\ 3 \\ -2\end{array}\right]$ Is $ B A$ defined?
In order for multiplication of two matrices to be defined, the two inner dimensions must be equal. If the two matrices have dimensions $( m \times  n)$ and $( p \times q)$ , then $ n$ (number of columns in the first matrix) must equal $ p$ (number of rows in the second matrix) for their product to be defined. How many columns does the first matrix, $ B$ , have? How many rows does the second matrix, $ A$ , have? Since $ B$ has a different number of columns (2) than $ A$ has rows (3), $ B A$ is not defined.